Question

Hi can someone help me with this geometry question I already got the first part but I don’t know about the last two

Answer 1

The Solution:

Given the properties:

Circle A:

`\begin{gathered} \text{ Center(a,b)=(}0,0) \\ \text{ radius r=6} \end{gathered}`

By the formula for the equation of a circle,

`(x-a)^2+(y-b)^2=r^2`

But

`a=0,b=0,r=6`

Substituting, we get

`\begin{gathered} (x-0)^2+(y-0)^2=6^2 \\ x^2+y^2=6^2 \end{gathered}`

For Circle B:

`\begin{gathered} \text{ Center(a,b)=(-4,-2)} \\ \text{ radius r=4} \end{gathered}`

Substituting these values in the formula for the equation of a circle.

`\begin{gathered} (x--4)^2+(y--2)^2=4^2 \\ (x+4)^2+(y+2)^2=4^2 \end{gathered}`

Graphing the two circles using the Desmos graph plotter, we have

Part B:

The transformation is a dilation by a scale factor of 4/6 (a shrink of circle A) and was shifted by 4 units left and 2 units down.

Part C:

The mapping shows that circle B is a shrink of circle A.

Circle A has its center at the origin (0,0) while the center of circle B is at (-4,-2)